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Quantifying Dynamic Stability of Genetic Memory Circuits
May-June 2012 (vol. 9 no. 3)
pp. 871-884
Peng Li, Dept. of Electr. & Comput. Eng., Texas A&M Univ., College Station, TX, USA
Yong Zhang, Dept. of Electr. & Comput. Eng., Texas A&M Univ., College Station, TX, USA
Garng M. Huang, Dept. of Electr. & Comput. Eng., Texas A&M Univ., College Station, TX, USA
Bistability/Multistability has been found in many biological systems including genetic memory circuits. Proper characterization of system stability helps to understand biological functions and has potential applications in fields such as synthetic biology. Existing methods of analyzing bistability are either qualitative or in a static way. Assuming the circuit is in a steady state, the latter can only reveal the susceptibility of the stability to injected DC noises. However, this can be inappropriate and inadequate as dynamics are crucial for many biological networks. In this paper, we quantitatively characterize the dynamic stability of a genetic conditional memory circuit by developing new dynamic noise margin (DNM) concepts and associated algorithms based on system theory. Taking into account the duration of the noisy perturbation, the DNMs are more general cases of their static counterparts. Using our techniques, we analyze the noise immunity of the memory circuit and derive insights on dynamic hold and write operations. Considering cell-to-cell variations, our parametric analysis reveals that the dynamic stability of the memory circuit has significantly varying sensitivities to underlying biochemical reactions attributable to differences in structure, time scales, and nonlinear interactions between reactions. With proper extensions, our techniques are broadly applicable to other multistable biological systems.

[1] D. Endy, "Foundations for Engineering Biology," Nature, vol. 438, pp. 449-453, 2005.
[2] J. Hasty, D. McMillen, and J.J. Collins, "Foundations for Engineering Biology," Nature, vol. 420, pp. 224-230, 2002.
[3] T. Gardner, C. Cantor, and J. Collins, "Construction of a Genetic Toggle Switch in Escherichia Coli," Nature, vol. 403, pp. 339-342, Jan. 2000.
[4] M.R. Atkinson, M.A. Savageau, J.T. Myers, and A.J. Ninfa, "Development of Genetic Circuitry Exhibiting Toggle Switch or Oscillatory Behavior in Escherichia coli," Cell, vol. 113, pp. 597-607, 2003.
[5] G. Fritz, N.E. Buchler, T. Hwa, and U. Gerland, "Designing Sequential Transcription Logic: A Simple Genetic Circuit for Conditional Memory," Systems and Synthetic Biology, vol. 1, pp. 89-98, 2007.
[6] L. Pollack and W.W. Webb, "Complex Molecular Dynamics in the Spotlight," Nature Biotechnology, vol. 28, pp. 564-565, 2010.
[7] C. Schöfer and K. Weipoltshammer, "Gene Dynamics and Nuclear Architecture during Differentiation," Differentiation, vol. 76, pp. 41-56, 2008.
[8] R.K. Chesser, "Heteroplasmy and Organelle Gene Dynamics," Genetics, vol. 150, pp. 1309-1327, Nov. 1998.
[9] S. Faisal, G. Lichtenberg, and H. Werner, "Polynomial Models of Gene Dynamics," Neurocomputing, vol. 71, pp. 2711-2719, 2008.
[10] Y. Zhang and P. Li, "Gene-Regulatory Memories: Electrical-Equivalent Modeling, Simulation and Parameter Identification," Proc. IEEE/ACM Int'l Conf. Computer-Aided Design (CAD), pp. 491-496, Nov. 2009.
[11] S. Widder, J. Macía, and R. Solé, "Monomeric Bistability and the Role of Autoloops in Gene Regulation," PLoS ONE, vol. 4, p. e5399, Apr. 2009.
[12] N. Nguyen, C. Myers, H. Kuwahara, C. Winstead, and J. Keener, "Design and Analysis of a Robust Genetic Muller C-Element," J. Theoretical Biology, vol. 264, pp. 174-187, 2010.
[13] P.S. Swain, M.B. Elowitz, and E.D. Siggia, "Intrinsic and Extrinsic Contributions to Stochasticity in Gene Expression," Proc. Nat'l Academy of Sciences USA, vol. 99, pp. 12795-12800, Oct. 2002.
[14] J.M. Raser and E.K. O'Shea, "Noise in Gene Expression: Origins, Consequence, and Control," Science, vol. 309, pp. 2010-2013, 2005.
[15] J.M. Pedraza and A. van Oudenaarden, "Noise Propagation in Gene Networks," Science, vol. 307, pp. 1965-1969, 2005.
[16] A. Colman-Lerner, A. Gordon, E. Serra, T. Chin, O. Resnekov, D. Endy, C.G. Pesce, and R. Brent, "Regulated Cell-to-Cell Variation in a Cell-Fate Decision System," Nature, vol. 437, pp. 699-706, 2005.
[17] W. Dong, P. Li, and G.M. Huang, "SRAM Dynamic Stability: Theory, Variability and Analysis," Proc. IEEE/ACM Int'l Conf. Computer-Aided Design (CAD), pp. 378-385, Nov. 2008.
[18] A. Funahashi, N. Tanimura, M. Morohashi, and H. Kitano, "Celldesigner: A Process Diagram Editor for Gene-regulatory and Biochemical Networks," BIOSILICO, vol. 1, no. 5, pp. 159-162, Nov. 2003.
[19] N.H.E. Weste and D. Harris, CMOS VLSI Design: A Circuit and Sysmtems Perspective, third ed. Pearson Education, Inc., 2005.
[20] Y. Zhang, P. Li, and G.M. Huang, "Separatrix in High-Dimensional State Space: System-Theoretical Computation and Application to SRAM Dynamic Stability Analysis," Proc. IEEE/ACM 47th Design Automation Conf. (DAC), pp. 567-572, June 2010.
[21] J. Zaborszky, G. Huang, B. Zheng, and T.C. Leung, "On the Phase Portrait of a Class of Large Nonlinear Dynamic Systems Such as the Power System," IEEE Trans. Automatic Control, vol. 33, no. 1, pp. 4-15, Jan. 1988.
[22] H.K. Khalil, Nonlinear Dynamics, second ed. Prentice Hall, 1996.
[23] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, 2003.
[24] M. Laurent and N. Kellershohn, "Multistability: A Major Means of Differentiation and Evolution in Biological Systems," Trends in Biochemical Science, vol. 24, pp. 418-422, Nov. 1999.
[25] A. Becskei, B. Séraphin, and L. Serrano, "Positive Feedback in Eukaryotic Gene Networks: Cell Differentiation by Graded to Binary Response Conversion," The EMBO J., vol. 20, pp. 2528-2535, 2001.
[26] J.E. Ferrell, "Self-perpetuating States in Signal Transduction: Positive Feedback, Double-Negative Feedback and Bistability," Current Opinion in Cell Biology, vol. 14, pp. 140-148, Apr. 2002.
[27] A.D. Hernday, B.A. Braaten, and D.A. Low, "The Mechanism by Which DNA Adenine Methylase and PapI Activate the Pap Epigenetic Switch," Molecular Cell, vol. 12, pp. 947-957, Oct. 2003.
[28] G. Huang, H. Wang, S. Chou, X. Nie, J. Chen, and H. Liu, "Bistable Expression of WOR1, a Master Regulator of Whiteopaque Switching in Candida albicans," Proc. Nat'l Academy of Sciences USA, vol. 103, pp. 12813-12818, Aug. 2006.

Index Terms:
system theory,biochemistry,cellular biophysics,genetics,noise,multistable biological systems,quantifying dynamic stability,biological functions,synthetic biology,injected DC noises,biological networks,genetic conditional memory circuit,dynamic noise margin concepts,system theory,noisy perturbation,static counterparts,cell-cell variations,parametric analysis,biochemical reactions,nonlinear interactions,Noise,Proteins,Circuit stability,Genetics,Stability analysis,Integrated circuit modeling,RNA,dynamic noise margin.,Dynamic stability,genetic memory,gene circuit
Citation:
Peng Li, Yong Zhang, Garng M. Huang, "Quantifying Dynamic Stability of Genetic Memory Circuits," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. 3, pp. 871-884, May-June 2012, doi:10.1109/TCBB.2011.132
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